Understanding Ohm's Law and Pouillet's Law 


1. Ohm's Law 

Formula: 
 
V = I * R 
 

Where: 

• • V: Voltage across the conductor (in volts).
  • I: Current flowing through the conductor (in amperes).
  • R: Resistance of the conductor (in ohms).

 

Explanation: 
Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across those points and inversely proportional to the resistance of the conductor. 

Applications: 

• • Calculating current in electrical circuits.
  • Designing resistors and selecting appropriate materials for circuits.
  • Understanding voltage drops in electrical networks.

 

---

2. Pouillet's Law (Formula for Resistance) 

Formula: 
 
R = (ρ * L) / A 
 

Where: 

• • R: Resistance of the conductor (in ohms).
  • ρ (rho): Resistivity of the material (in ohm-meters or ohm-centimeters).
  • L: Length of the conductor (in meters or centimeters).
  • A: Cross-sectional area of the conductor (in square meters or square centimeters).

 

Explanation: 
Pouillet's Law provides the relationship between the resistance of a material and its physical dimensions (length and cross-sectional area) as well as its intrinsic property, resistivity. 

Applications: 

• • Calculating the resistance of wires and cables in various applications.
  • Choosing materials with appropriate resistivity for specific electrical applications.
  • Analyzing the effects of length and cross-sectional area on resistance in power transmission lines.

 

---

Combined Application in Electrical Systems: 
These laws are often used together to design and analyze electrical circuits and systems: 

• • Use Pouillet's Law to calculate the resistance of a wire based on its material, length, and cross-sectional area.
  • Apply Ohm's Law to determine how this resistance affects the current and voltage in the circuit.

 

Example Calculation: 
Consider a copper wire with the following properties: 

• • Resistivity (ρ): 1.68 × 10⁻⁸ ohm-meters
  • Length (L): 100 meters
  • Cross-sectional area (A): 1 mm² (1 × 10⁻⁶ m²)

 

Step 1: Calculate Resistance Using Pouillet's Law 
 
R = (ρ * L) / A 
R = (1.68 × 10⁻⁸ * 100) / (1 × 10⁻⁶) 
R = 1.68 ohms 
 

Step 2: Calculate Current Using Ohm's Law 
Assume the wire is connected to a 12V battery: 
 
I = V / R 
I = 12 / 1.68 
I ≈ 7.14 A 
 

Result: The current flowing through the wire is approximately 7.14 amperes. 

---

Conclusion 
Ohm's Law and Pouillet's Law are foundational principles in electrical engineering, enabling precise calculations and effective circuit design. By understanding these laws, engineers can optimize electrical systems for efficiency, safety, and reliability.